Multiplying and Dividing Listen & Learn PRESENTED BY MATHMANIAC Mathematics, Grade 8

(1)

Listen & Learn

Mathematics, Grade 8

PRESENTED BY MATHMANIAC

Multiplying and Dividing

Listen & Learn

PRESENTED BY MATHMANIAC

Mathematics, Grade 8

Integers – Multiplying and Dividing

Introduction

• Welcome to today’s topic

• Parts of Listen & Learn

(2)

What you will learn

After viewing this presentation, you

will be able to

• multiply and divide integers using one

of two methods: the table method or

the like/unlike method.

Agenda

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

(3)

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

Real-life applications

• You can apply

knowledge of integers

to real-life situations,

such as temperature,

(4)

Agenda

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

Definition and Terms

Integer

The set of all positive and negative whole

numbers and zero.

For example, +75, –112, 0, +3, –24 are

considered integers, but 1½ and 112.76

are NOT considered integers.

(5)

Number Lines

The whole numbers you use every day

that are greater than zero are positive

integers.

The number line you may be familiar with

begins at zero and moves to the right.

Definitions and Terms

Integer Number Line

The integer number line includes the

negative numbers (numbers that are less

than zero).

(6)

Agenda

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

Agenda

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

(7)

Solve: +7 x (+3)

+

–

+

–

+

÷

x

Operation

Symbol for

1

st

_integer

Symbol for

2

nd

_integer

Result

Solve:

+

7 x (

+

3)

Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive.

–

+

x

Methods to x and

(8)

+

–

+

–

+

x

Methods to x and

Integers: Table Method

Solve:

+

7 x (

+

3)

Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive.

Solve:

+

7 x (

+

3)

Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. The answer ispositive.

+

–

+

–

+

x

Methods to x and

(9)

Solve: +7 x (+3)

Step 2: Multiply the numbers as you normally would. 7 x 3 = +21

+

–

+

–

+

x

Solve:

–

7 x (

+

3)

Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive.

–

+

x

Methods to x and

(10)

Solve:

–

7 x (

+

3)

Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive.

+

–

+

–

+

x

Methods to x and

Integers: Table Method

Solve:

–

7 x (

+

3)

Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. The answer isnegative.

+

–

+

–

+

x

Methods to x and

(11)

Solve: –7 x (+3)

Step 2: Multiply the numbers as you normally would. 7 x 3 =21

+

–

+

–

+

x

Solve: –7 x (+3)

Step 3: You know your answer is negative and the product is 21. Put these together to get an answer of–21.

–

+

x

Methods to x and

(12)

Let’s try another question.

Solve: –12 x (–5)

+

–

+

–

+

x

Methods to x and

Integers: Table Method

Solve:

–

12 x (

–

5)

Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is also negative. Therefore, you are multiplying a negative by a negative. The answer ispositive.

+

–

+

–

+

x

Methods to x and

(13)

Solve:

–

12 x (

–

5)

Step 2: Multiply the numbers as you normally would. 12 x 5 = 60

+

–

+

–

+

x

Solve:

–

12 x (

–

5)

Step 3: You know your answer is positive and the product is 60. Put these together to get an answer of+60.

–

+

x

Methods to x and

(14)

Solve:

–

9/(

+

3) =

–3

Now solve for integer division.

+

–

+

–

+

÷

Methods to x and

Integers: Table Method

Did you notice a pattern?

–

+/–

+

–/–

–

–/+

+

+/+

Methods to x and

(15)

• Real-life applications

• Definition and terms

• Methods to multiply and divide

integers

• Table method

• Like/unlike method

• Extensions

Methods to x and Integers:

Like/Unlike Method

Solve +28/(–7)

Step 1: Look at the symbols of the

numbers that you are dividing (or

multiplying).

(16)

Solve +28/(–7)

Step 1: Look at the symbols of the

numbers that you are dividing (or

multiplying).

Step 2: Are the symbols the same or are

they different?

Methods to x and Integers:

Like/Unlike Method

Solve +28/(–7)

Step 1: Look at the symbols of the

numbers that you are dividing (or

multiplying).

Step 2: Are the symbols the same or are

they different?

• If the symbols are the same the

answer will be POSITIVE (+).

• If the symbols are different the

answer will be NEGATIVE (–).

Methods to x and Integers:

Like/Unlike Method

(17)

Solve +28/(–7)

Step 1: Look at the symbols of the

numbers that you are dividing (or

multiplying).

Step 2: Are the symbols the same or are

they different?

• If the symbols are the same the

answer will be POSITIVE (+).

• If the symbols are different the

answer will be NEGATIVE (–).

Step 3: Divide (or multiply) as you normally

would and use the sign from step 2.

Solve +28/(–7)

Step 1: Look at the symbols of the numbers

that you are dividing (or multiplying).

Methods to x and Integers:

Like/Unlike Method

(18)

Methods to x and Integers:

Like/Unlike Method

Solve +28/(–7)

Step 1: Look at the symbols of the numbers

that you are dividing (or multiplying).

Step 2: Are the symbols the same or are they

different?

They are different.

Methods to x and Integers:

Like/Unlike Method

Solve +28/(–7)

Step 1: Look at the symbols of the numbers

that you are dividing (or multiplying).

Step 2: Are the symbols the same or are they

different?

• If the symbols are the same the

answer will be POSITIVE (+).

• If the symbols are different the

answer will be NEGATIVE (–).

(19)

Solve +28/(–7)

Step 1: Look at the symbols of the numbers

that you are dividing (or multiplying).

Step 2: Are the symbols the same or are they

different?

• If the symbols are the same the

answer will be POSITIVE (+).

• If the symbols are different the

answer will be NEGATIVE (–).

Step 3: Divide (or multiply) as you normally

would and use the sign from step 2.

+28/(–7) =

–4

Let’s apply what you’ve

learned.

You read the weather report

for today and it says that it

(20)

You read the weather report for today and it

says that it will be 16 degrees Celsius in the

morning. The report predicts that the high for

the day will be double the morning

temperature. What is the predicted high?

Step 1: Write out the question.

+16 x (+2)

Methods to Solve Equations

You read the weather report for today and it

says that it will be 16 degrees Celsius in the

morning. The report predicts that the high for

the day will be double the morning

temperature. What is the predicted high?

Step 2: Look at the symbols. Are they the

same or different?

+

16 x (

+

2)

Both symbols are positive, therefore they are

the same.

(21)

You read the weather report for today and it

says that it will be 16 degrees Celsius in the

morning. The report predicts that the high for

the day will be double the morning

temperature. What is the predicted high?

Step 3: Multiply the numbers as you normally

would and take the symbol from

step 2 (+).

+16 x (+2) = +32

Agenda

• Real-life applications

• Definition and terms

(22)

Extensions

• Integer problems involving:

 Order of operations

 Square roots and exponents

 Addition and subtraction

 Multiplication and division

 Solving equations

Questions

When multiplying integers, if the symbols

are the same, will the answer be positive

or negative?

a) positive

b) negative

(23)

When multiplying integers, if the symbols

are the same, will the answer be positive

or negative?

a) positive

b) negative

Questions

When multiplying integers, if the symbols

are the same, will the answer be positive

or negative?

(24)

Questions

When dividing integers, if the symbols are

different, will the answer be positive or

negative?

a) positive

b) negative

Questions

When dividing integers, if the symbols are

different, will the answer be positive or

negative?

a) positive

(25)

When dividing integers, if the symbols are

different, will the answer be positive or

negative?

a) positive

b) negative

Whenever the symbols are different, the answer

is negative. This rule only applies when we are

multiplying or dividing two numbers.

Questions

When solving the expression –5y x (–10)

will the answer will be positive or

negative?

a) positive

(26)

Questions

When solving the expression –5y x (–10)

will the answer will be positive or

negative?

a) positive

b) negative

The answer is positive because both symbols

are the same. This rule only applies when we

are multiplying or dividing two numbers.

Resources

Math League: Integer Help

http://www.mathleague.com/help/

integers/integers.htm

Math: Integer Lessons

http://www.math.com/school/subject1/less

ons/S1U1L12GL.html

NLVM: Integer Multiplication

http://nlvm.usu.edu/EN/NAV/frames_asid_

322_g_2_t_1.html?from=grade_g_2.html